Also, it helps to think about an extreme case. Let's say you've got two readings:
Reading one increases by one unit from 1 to 2 - an increase of 100%
Reading two increases by one unit from 100 to 101 - an increase of 1%
The average of those two averages is 50.5%. But we know that the total didn't increase by 50.5% - after all, all we did was add 2 to 101, which was an increase of just under 2%